where \(a_n\)  denotes the coefficient of the \(n\) -degree term. The form of \(M_{qq}\)  is constrained by polymer symmetries. Therefore, since the polymer does not have a preferred transverse direction (it can have a preferred longitudinal direction though due to the polarity [1]}) \(M_{qq}\)  must be an even function of \(q\) . The term \(a_0\)  stands for the mobility for the \(q=0\)  mode (infinite wavelength). For transient networks, the value of \(a_0\)  must be 0. The reason for this can be seen from Fig. REF (b), where we sketch the relaxation process of a long-wavelength mode. In order to relax such a mode, multiple successive unbinding events are required, indicating that transient crosslinkers impose stronger limitations to long-wavelength modes, leading to smaller mobilities. In order to relax the infinite-wavelength mode there should be infinite successive binding events, each of them takes finite time, therefore leading to zero mobility. Hence, the leading term in Eq. (REF ) is the quadratic term, and for small \(q\)  we have \(M_{qq}=a_2 q^2\) .
